Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture
Representation Theory
2024-02-27 v4 Algebraic Geometry
Abstract
We show that the specialized quantum D-module of the equivariant quantum cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the D-module of graded traces on the minimal nilpotent orbit in the Lie algebra of the same type. This generalizes a recent result of Shlykov [Hikita conjecture for the minimal nilpotent orbit, to appear in Proc. AMS, https://doi.org/10.1090/proc/15281] and hence verifies in this case the quantum version of Hikita's conjecture, proposed by Kamnitzer, McBreen and Proudfoot [The quantum Hikita conjecture, Advances in Mathematics 390 (2021) 107947]. We also show analogous isomorphisms for singularities of BCFG type.
Keywords
Cite
@article{arxiv.2302.13249,
title = {Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture},
author = {Xiaojun Chen and Weiqiang He and Sirui Yu},
journal= {arXiv preprint arXiv:2302.13249},
year = {2024}
}